S 3 4 solution 1 even though we are not explicitly

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: minutes and 7 seconds (which is 127 seconds) the period T = 1 (127) = 127 seconds. Hence, the 2 2 4π angular frequency is ω = 2π = 127 radians per second. Putting these two pieces of information T 4π together, we have that y = 64 sin 127 t describes the y -coordinate on the Giant Wheel after t seconds, assuming it is centered at (0, 0) with t = 0 corresponding to the point Q. In order to find an expression for h, we take the point O in the figure as the origin. Since the base of the Giant Wheel ride is 8 feet above the ground and the Giant Wheel itself has a radius of 64 feet, its center is 72 feet above the ground. To account for this vertical shift upward,4 we add 72 to our formula 4π for y to obtain the new formula h = y + 72 = 64 sin 127 t + 72. Next, we need to adjust things so that t = 0 corresponds to the point P instead of the point Q. This is where the phase comes into play. Geometrically, we need to shift the angle θ in the figure back π radians. From Section 10.2.1, 2 4π we know θ = ωt = 12...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online